What Does “Sufficient Mass” Mean in Newton's Gravitational Equation?: Stanford Physics Department Elucidates on How The Separation Distance is Quadratic and the Size of the Two Masses is Crucial

The force of Gravity is directly proportional to the size of BOTH object's mass:

In The Heliocentric Model, Gravity is a non-contact vector (a pseudo-force that can be exerted on a body without touching it), a vector force that even Sir Issac Newton, himself, stated could not exists across a vacuum in his letter to Bentley in 1691.

Episode 2 - The Gravitational Constant - Brian Mullin:

In Newton’s letters to Bentley, he was hoping to prove the existence of God. (A Deity):

In preparing his sermons, Bentley had received Newton’s recommendations, in July 1691, for background information from parts of the Principia which had been published about five years earlier. After Bentley gave his oral presentations, but before publishing them, he consulted with Isaac Newton in several letters, clarifying a number of points regarding Gravity and Cosmogony, so that he could be sure the printed version of his lectures gave a correct interpretation of Newton’s ideas.

The summation of all those correspondences comes to this quote:

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate Gravity to me.

That Gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it.

Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers.”

                        --Sir Isaac Newton: Letters to Bentley, February 1693

From Stanford Physics Department

The Four Fundamental non-contact forces in The Standard Model Are:

1. The gravitational force

2. The electromagnetic force (the force between charged particles or poles of magnets)

3. The weak nuclear force

4. The strong nuclear force

“The latter two are active only at distances as small as those present between protons and neutrons in the nuclei of atoms. Sometimes a non-contact force is called "force at a distance."

Unlike the other three forces, gravity is a purely an attractive force. If we bring a negative and a positive charge together, the electrostatic force is attractive (brings them together). But if we bring two positive charges or two negative charges together, they repel one another (opposites attract, likes repel). There is no such repulsive component to the gravitational force; you never see someone walking down the street suddenly get ejected from the planet by gravity.”

The Universal Law of Gravitation

The Universal Law of Gravitation says that the force, Fg, between two objects of mass m1 and m2 is directly proportional to the product of the SIZE of the masses and inversely proportional to the square of the distance, r, between them.

The proportionality constant is:

G = 6.674 x 10-11 N·m2Kg-2

The Gravitational Constant “G”

The gravitational constant, “G”, is claimed to be a fundamental constant of the universe. You can think of such constants as fixed numbers that are there for us to get the units correct. When we multiply two masses and divide by a length squared, we need to end up with units of force (1N = 1 Kg·m/s2). If we used different units, G would be different. What's important is the proportionality of the SIZE of the masses and the distance to the gravitational force.

Dependence of Gravitational Force on Substantial Mass and Distance

The images below shows how the force of gravity (Fg) varies as one of the masses is increased from zero and the other is held constant. Fg is directly and linearly proportional to each mass. Thus, the linear graph show how a Sufficient Mass must be achieved in order for Newton’s Gravitational Attraction to become applicable.

The Universal Law of Gravitation is called an inverse-square law because the force is inversely proportional to the square of the distance between two masses. We will see another inverse square law when we study the electrostatic force.

We generally think of gravity in terms of one variable mass and one fixed mass, like a planet. The force of gravity is greater on a more massive person than a less massive person, therefore the more massive person weighs more. Weight, unlike mass, is a measure of force.

For instance, the gravitational force on The Moon is 1/6 that on Earth because the mass of the moon is about 1/6 the mass of Earth, thereby again illustrating how a Sufficient Mass must be achieved in order for Newton’s Gravitational Attraction equations to become applicable.  

The important thing about this feature of gravity is that if we double the distance between objects, the force of gravity is reduced by a factor of four (22), not two. The graph shows that when r, the distance between masses, is small, the gravitational force is high, but as r is increased, the force drops non-linearly, which again illustrates how a Sufficient Mass must be achieved between BOTH bodies for Newton’s Gravitational Laws to remain applicable. At the atonic level, no Gravity is said to exits.

There are only electrostatic forces. And, if we bring a negative and a positive charge together, the electrostatic force is attractive (brings them together). But if we bring two positive charges or two negative charges together, they repel one another (opposites attract, likes repel). There is no such repulsive component to the gravitational force.

Again, The Separation Distance is Quadratic

The important thing about this feature of gravity is that if we double the distance between objects, the force of gravity is reduced by a factor of four (22), not two. The graph shows that when r, the distance between masses, is small, the gravitational force is high, but as r is increased, the force drops non-linearly.

The Separation Distance is Quadratic: